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A diagrammatic approach to string polytopes

2020/11/24 by Steinert, Christian
#Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2011.12003

Abstract

We prove that for every complex classical group G the string polytope associated to a special reduced decomposition and any dominant integral weight λ will be a lattice polytope if and only if the highest weight representation of the Lie algebra of G with highest weight λ integrates to a representation of G itself. This affirms an earlier conjecture and shows that every partial flag variety of a complex classical group admits a flat projective degeneration to a Gorenstein Fano toric variety.

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